So far, ABC’s new detective thriller set in 1980s Los Angeles relies more on suspense than explicit gore.

Only a network press release could describe a serial killer as a “tragic soul,” which ABC does in a promotion for its new thriller “Wicked City.” But the series, which opens in 1982 Los Angeles, mostly rises above that level of soul-sucking banality. It is an invitation instead to fear for the young women in Sunset Strip clubs who have been targeted by a predator, and to root for police who are trying to find him before he can decapitate another girl.

The fact that the audience knows almost from the beginning who the killer...